Context. Contemporary high precision photometry from space provided by the Kepler and CoRoT satellites generates significant breakthroughs in terms of exploiting the long-period, g-mode pulsating hot B subdwarf (sdBVs) stars with asteroseismology. Aims: We present a detailed asteroseismic study of the sdBVs star KIC02697388 monitored with Kepler, using the rich pulsation spectrum uncovered during the ~27-day-long exploratory run Q2.3. Methods: We analyse new high-S/N spectroscopy of KIC02697388 using appropriate NLTE model atmospheres to provide accurate atmospheric parameters for this star. We also reanalyse the Kepler light curve using standard prewhitening techniques. On this basis, we apply a forward modelling technique using our latest generation of sdB models. The simultaneous match of the independent periods observed in KIC02697388 with those of models leads objectively to the identification of the pulsation modes and, more importantly, to the determination of some of the parameters of the star. Results: The light curve analysis reveals 43 independent frequencies that can be associated with oscillation modes. All the modulations observed in this star correspond to g-mode pulsations except one high-frequency signal, which is typical of a p-mode oscillation. Although the presence of this p-mode is surprising considering the atmospheric parameters that we derive for this cool sdB star (Teff = 25 395 ± 227 K, log g = 5.500 ± 0.031 (cgs), and log N(He) /N(H) = -2.767 ± 0.122), we show that this mode can be accounted for particularly well by our optimal seismic models, both in terms of frequency match and nonadiabatic properties. The seismic analysis leads us to identify two model solutions that can both account for the observed pulsation properties of KIC02697388. Despite this remaining ambiguity, several key parameters of the star can be derived with stringent constraints, such as its mass, its H-rich envelope mass, its radius, and its luminosity. We derive the properties of the core proposing that it is a relatively young sdB star that has burnt less than ~34% (in mass) of its central helium and has a relatively large mixed He/C/O core. This latter measurement is in line with the trend already uncovered for two other g-mode sdB pulsators analysed with asteroseismology and suggests that extra mixing is occurring quite early in the evolution of He cores on the horizontal branch. Conclusions: Additional monitoring with Kepler of this particularly interesting sdB star should reveal the inner properties of KIC02697388 and provide important information about the mode driving mechanism and the helium core properties. Tables 3 and 4 are available in electronic form at http://www.aanda.org